(x2-2x-3)+3.\(\sqrt{x-3}.\sqrt{x-3}.\sqrt{\dfrac{x+1}{x-3}}=7-3=4\)
=>(x+1)(x-3)+3.\(\sqrt{x-3}.\sqrt{x+1}=4\)
Dat \(\sqrt{x-3}.\sqrt{x+1}=a\left(a>0\right)\)
=>(x+1)(x-3)=a2
pt<=> a2+3a-4=0
=> (a+4)(a-1)=0
=> \(\left[{}\begin{matrix}a+4=0\\a-1=0\end{matrix}\right.\)
=>. \(\left[{}\begin{matrix}a=-4\left(KTM\right)\\a=1\left(TM\right)\end{matrix}\right.\)
Voi a=1 thi (x+1)(x-3)=1
=> x2-2x-3-1=0
=> (x2-2x+1)-5=0
=> (x-1)2=5
=> \(\left[{}\begin{matrix}x-1=\sqrt{5}\\x-1=-\sqrt{5}\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}x=\sqrt{5}+1\\x=-\sqrt{5}+1\end{matrix}\right.\)
